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Rotating Quadrilaterals and Triangles: Guide to 120° and 270° Transformations

This guide provides step-by-step instructions for rotating quadrilaterals and triangles using coordinate rules. Specifically, it demonstrates how to rotate the quadrilateral RSTU and triangle JKL about a point or the origin by given angles. The process includes drawing segments, angles, and new vertices based on rotation rules (120° and 270°). Examples and practice problems are included to reinforce learning. By following these steps, students will master the concepts of geometric transformations and understand the application of rotation in coordinate geometry.

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Rotating Quadrilaterals and Triangles: Guide to 120° and 270° Transformations

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  1. o Draw a 120 rotation of ABCabout P. STEP 1 Draw a segment from Ato P. EXAMPLE 1 Draw a rotation SOLUTION

  2. o Draw a ray to form a 120 angle with PA. STEP 3 DrawA′ so thatPA′= PA. EXAMPLE 1 Draw a rotation STEP 2

  3. EXAMPLE 1 Draw a rotation STEP 4 Repeat Steps 1– 3 for each vertex. DrawA′B′C′.

  4. Graph quadrilateral RSTUwith vertices R(3, 1),S(5, 1), T(5, –3), and U(2, –1). Then rotate the quadrilateral 270 about the origin. o o Graph RSTU. Use the coordinate rule for a 270 rotation to find the images of the vertices. (a, b) (b, –a) R′(1, –3) R(3, 1) S(5, 1) S′(1, –5) T(5, –3) T′(–3, –5) U(2, –1) U′(–1, –2) EXAMPLE 2 Rotate a figure using the coordinate rules SOLUTION Graph the image R′S′T′U′.

  5. 1. Trace DEFand P. Then draw a 50°rotation of ANSWER DEFabout P. for Examples 1 and 2 GUIDED PRACTICE

  6. ANSWER for Examples 1 and 2 GUIDED PRACTICE 2. Graph JKLwith vertices J(3, 0), K(4, 3), and L(6, 0). Rotate the triangle 90° about the origin.

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